Adaptive weighting method for orthogonal frequency division multiplexed soft symbols using channel state information estimates

ABSTRACT

A method for weighting orthogonal frequency division multiplexed soft symbols is provided, including the steps of receiving a plurality of sub-carriers modulated by digital information and filtering the sub-carriers to produce complex soft decision outputs. The magnitudes of the soft decision outputs are used to creating a first sequence of data. The differences between successive samples in the first sequence are used to create a second sequence of data. The first and second sequences are filtered and compensated for differences in effective group delay of the first and second sequences to produce third and fourth sequences. Then these third and fourth sequences are used to determine a plurality of weights and the weights are applied to the complex soft decision outputs. A receiver which incorporates the method is also disclosed.

BACKGROUND OF THE INVENTION

This invention relates to signal processing, and more particularly, tosignal processing techniques for use in Digital Audio Broadcasting (DAB)systems.

Digital Audio Broadcasting is a medium for providing digital-qualityaudio, superior to existing analog broadcasting formats. Both AM and FMDAB signals can be transmitted in a hybrid format where the digitallymodulated signal coexists with the currently broadcast analog AM or FMsignal, or in an all-digital format without an analog signal.In-band-on-channel (IBOC) DAB systems require no new spectralallocations because each DAB signal is simultaneously transmitted withinthe same spectral mask of an existing AM or FM channel allocation. IBOCpromotes economy of spectrum while enabling broadcasters to supplydigital quality audio to their present base of listeners. Several IBOCDAB approaches have been suggested. One such approach, set forth in U.S.Pat. No. 5,588,022, presents a method for simultaneously broadcastinganalog and digital signals in a standard AM broadcasting channel. Usingthis approach, an amplitude-modulated radio frequency signal having afirst frequency spectrum is broadcast. The amplitude-modulated radiofrequency signal includes a first carrier modulated by an analog programsignal. Simultaneously, a plurality of digitally-modulated carriersignals are broadcast within a bandwidth which encompasses the firstfrequency spectrum. Each digitally-modulated carrier signal is modulatedby a portion of a digital program signal. A first group of thedigitally-modulated carrier signals lies within the first frequencyspectrum and is modulated in quadrature with the first carrier signal.Second and third groups of the digitally-modulated carrier signals lieoutside of the first frequency spectrum and are modulated both in-phaseand in-quadrature with the first carrier signal. Multiple carriers areemployed by means of orthogonal frequency division multiplexing (OFDM)to bear the communicated information.

FM IBOC broadcasting systems using have been the subject of severalUnited States patents including U.S. Pat. No. 5,465,396; 5,315,583;5,278,844 and 5,278,826. In addition, a commonly assigned pending patentapplication for a “Method and System for Simultaneously Broadcasting andReceiving Digital and Analog Signals, by D. Kumar and B. Hunsinger, Ser.No. 08/274,140, filed Jul. 1994 discloses an FM IBOC DAB system, nowU.S. Pat. No 5,956,624.

The signals used in Digital Audio Broadcasting are subject to fading andnoise (interference). Digital Audio Broadcasting receivers may includeViterbi decoders. Conventional implementations of soft-decision Viterbidecoders rely on constant signal and gaussian noise statistics for(near) optimum decoding. Practically these statistics should be nearlyconstant over the path memory of the Viterbi decoder, or the span of theinterleaver, whichever is greater. An interleaver may be used to yieldstatistical independence of the fading statistics of the soft symbolsover the path memory of the Viterbi decoder after deinterleaving. Theremedy for a flat fading channel causing fluctuating signal levels withconstant noise is well known. However, there exists a need for a signalprocessing technique that can address independently varying signal andnoise levels.

SUMMARY OF THE INVENTION

A method for weighting orthogonal frequency division multiplexed softsymbols is provided, including the steps of receiving a plurality ofsub-carriers modulated by digital information, filtering thesub-carriers to produce complex soft decision outputs, creating a firstsequence of the magnitudes of the complex soft decision outputs,determining the differences between successive samples in the firstsequence, creating a second sequence of the differences betweensuccessive samples in the first sequence, filtering the first and secondsequences and compensating for differences in effective group delay ofthe first and second sequences to produce third and fourth sequences,using the third and fourth sequences to determine a plurality ofweights, and applying the plurality of weights to the complex softdecision outputs. The invention also encompasses receivers thatincorporate the above method.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a diagram showing the steps in the method of this invention;and

FIG. 2 is a functional block diagram showing the mapping and processingof bits through a digital audio broadcasting receiver which employs themethod of this invention.

DESCRIPTION OF THE PREFERRED EMBODIMENTS

The present invention will be described in terms of the adaptiveweighting procedure for coherently detected quadrature phase shift keyed(QPSK) or binary phase shift keyed (BPSK) signals under various fadingconditions assuming gaussian noise or interference statistics.

For single carrier, flat fading signal, constant noise or interference,the flat fading channel multiplies the K^(th) interleaved symbol by afading factor a_(k), which is assumed to be constant over the symbolduration. The signal sample output of a matched filter in the receivercan be expressed as:

y _(k) =a _(k) ·x _(k) +n _(k)  (1)

where x_(k) is the transmitted signal component and n_(k) is thereceived noise. The appropriate weighting for that soft decision symbolat the receiver is itself a_(k), or more practically the receiver'sestimate â_(k). Therefore the soft symbol S_(k) entering a deinterleaverprior to the Viterbi decoder is presented as:

s _(k) =â _(k) ·y _(k)  (2)

The symbols immediately surrounding the k^(th) symbol are similarlyaffected by the relatively slowly varying fading. It is impossible toadequately estimate this fading factor over a single symbol because itis impossible to separate its statistics from the noise. However thefading factor can be estimated statistically using a weighted averageover a set of samples with correlated fading constants, specifically thesymbols that are temporally close to the k^(th) symbol.

Let the signal term x_(k) be complex whose real and imaginary componentsare binary valued at ±1. For reasonably large SNR, where the noise (orinterference) is approximated to be zero mean average white Gaussiannoise (AWGN), the fading factor might be estimated as: $\begin{matrix}\begin{matrix}{{\hat{a}}_{k} = {E\left\{ {y_{k}} \right\}}} \\{= {{E\left\{ {{{a_{k} \cdot x_{k}} + n_{k}}} \right\}} \cong {E\left\{ a_{k} \right\}}}}\end{matrix} & (3)\end{matrix}$

However, this estimate is not accurate for small SNR since the rectifiednoise will place a lower limit on â_(k). This limitation would reduceerasure effectiveness when the signal level fades to zero. The signallevel for coherent detection and Gaussian noise can be estimated usingan exact expression as a function of the second and fourth moments ofthe magnitude of y_(k) (i.e. E{|y_(k)|²} and E{|y_(k)|⁴}). These momentsare obtained through averaging or lowpass filtering of the squared orfourth power of the magnitude of y_(k). Assuming a constant AWG noisefloor, the weighting factor for the soft decision is equal to the fadingfactor:

â _(k)={square root over (2+L ·(E{|y| ²+L })² −E{|y| ⁴+L })}  (4)

This equation has been used to successfully estimate the signal level ina mobile satellite receiver.

For single carrier, flat fading signal, and flat fading interference,the difference between the constant signal and the flat fading signalappears as an interference fading factor σk. It is assumed that thefading of the signal and interference are approximately independent, andthe interference is approximated as AWGN. The Gaussian interferenceassumption is made in the absence of known precise statistics of theinterferer. Furthermore, this assumption becomes less objectionable whenwe recognize that the Viterbi decoder tends to “Gaussianize” the noiseor interference summed over the weighted symbols in its path memories.The soft-decision output of the matched filter can be expressed as:

y _(k) =a _(k) ·x _(k) +σ _(k) ·n _(k)  (5)

Dividing both sides by σ_(k) puts the expression in form familiar to thenonfaded interference case: $\begin{matrix}{\frac{y_{k}}{\sigma_{k}} = {{\frac{a_{k}}{\sigma_{k}} \cdot x_{k}} + n_{k}}} & (6)\end{matrix}$

Then the appropriate weight for the soft symbol is identified. The softsymbol entering the deinterleaver prior to the Viterbi decoder ispresented as: $\begin{matrix}{s_{k} = {\frac{{\hat{a}}_{k}}{{\hat{\sigma}}_{k}^{2}} \cdot y_{k}}} & (7)\end{matrix}$

The fading factor can be estimated as in equation (4). An additionalestimate of the noise variance σ̂_(k)²

is required for this weighting. This estimate can be computed as:$\begin{matrix}{{\hat{\sigma}}_{k}^{2} = {{E\left\{ {y_{k}}^{2} \right\}} - {\hat{a}}_{k}^{2}}} & (8)\end{matrix}$

For multiple sub-carriers (OFDM), selective fading signal, and selectivefading interference, the method of the present invention can bedescribed as follows. OFDM sub-carriers comprise a set of orthogonallyspaced (in frequency) sub-carriers, each modulated synchronously at thesymbol rate. QPSK sub-carrier modulation is assumed here, although otherlinear modulation techniques such as MPSK or QAM can be accommodatedwith modification. OFDM has been shown to be tolerant of multipathfading since the fading over any individual sub-carrier bandwidth isconsidered to be flat (flat fading requires no sub-carrierequalization). In a severe selective fading instance, a portion of theOFDM sub-carriers may be lost in a null while the remaining sub-carriersare recoverable. In contrast, wideband single carrier modulation canexperience the same spectral null where significant degradation canoccur over all the bits if equalization is not employed.

Each OFDM sub-carrier can be treated as an independent channel with flatfading signal and interference; however, this is not optimum. Thecorrelation of the signal and noise fading across sub-carriers nearby infrequency can be exploited to improve performance. This can beaccomplished through filtering the statistics across both time andfrequency surrounding any particular sub-carrier. The k^(th) symbol ofthe nt^(th) sub-carrier is weighted as: $\begin{matrix}{s_{k,n} = {\frac{{\hat{a}}_{k,n}}{{\hat{\sigma}}_{k,n}^{2}} \cdot y_{k,n}}} & (9)\end{matrix}$

where y_(k,n), is a complex soft symbol resulting from QPSK demodulationof the k^(th) symbol of the n^(th) sub-carrier. The only differencebetween equations (9) and (7) is the exploitation of the correlation ofadjacent sub-carrier statistics in equation (9). The fading factors canbe estimated after 2-dimensional smoothing (filtering across time andsub-carriers) of the following values:

U _(k,n) =E{|y _(k,n)|²}

V _(k,n) =E{|y _(k,n)|⁴}  (10)

Compute the symbol weighting factor for coherently detected QPSK as:$\begin{matrix}{w_{k,n} = \frac{\sqrt[4]{{2 \cdot u_{k,n}^{2}} - v_{k,n}}}{u_{k,n} - \sqrt{{2 \cdot u_{k,n}^{2}} - v_{k,n}}}} & (11)\end{matrix}$

where W_(k,n) is the weight to be used for the soft symbol prior todeinterleaving.

The adaptive weighting procedure for differentially detected QPSKsignals under various fading conditions will now be described. Theseresults can be extended to BPSK with minor modification.

The goal of the present invention is to maximize the resulting SNR ofthe weighted and combined symbols after differential detection into theViterbi decoder. This minimizes the probability of bit error at theoutput of the Viterbi decoder. The absolute optimization of theweighting of the soft decision statistic is a function of the particularViterbi decoder. Therefore the answer is not necessarily unique.Furthermore, since the Viterbi decoder tends to “Gaussianize” the pathmetrics over the path memories, then this technique tends to maximizethe SNR over the path memory.

A similar expression for the weighting factor can be derived assumingGaussian noise into a differential QPSK detector resulting innon-Gaussian statistics at the output. The fading factor can be computedas a function of the statistics of the output of the differentialdetector where we define the soft decision of the form:

S=(a+n ₁)·(a·e ^(j·φ) +n ₂)  (12)

where φ denotes the phase information imposed between a pair of adjacentsymbols in the differential encoding, and n are the independent noisesamples. The fading factor a of the adjacent symbols is assumed to beapproximately equal. The signal to noise ratio after differentialdetection is easily computed to be: $\begin{matrix}{{SNR} = \frac{a^{4}}{{2 \cdot a^{2} \cdot \sigma^{2}} + \sigma^{4}}} & (13)\end{matrix}$

The ideal weighting factor for the post-differentially detected symbolsis therefore: $\begin{matrix}{w = \frac{a^{2}}{{2 \cdot a^{2} \cdot \sigma^{2}} + \sigma^{4}}} & (14)\end{matrix}$

The first differential approach described here uses statisticalestimates of the second and fourth moments of the differentiallydetected symbols to form the weighting factor. The second and fourthmoments are described by the following previously known relationships.

E{|S| ²}=(a ²+σ²)²

E{|S| ⁴}=(a ⁴+4·a ²·σ² +2·σ ⁴)²  (15)

Then the fading factor can be estimated as: $\begin{matrix}{{\hat{a}}_{k} = \sqrt[4]{{{2 \cdot E}\left\{ {S_{k}}^{2} \right\}} - \sqrt{E\left\{ {S_{k}}^{4} \right\}}}} & (16)\end{matrix}$

and the noise can be estimated as: $\begin{matrix}{{\hat{\sigma}}_{k}^{2} = {\sqrt{E\left\{ {S_{k}}^{2} \right\}} - {\hat{a}}_{k}^{2}}} & (17)\end{matrix}$

The estimates of equations (16) and (17) are inserted into equation (14)to obtain the weight.

Simulations were performed using adaptive weighting as described inequations (14), (16), and (17). Although long-term estimates withoutfading yielded good results, a compromise must be reached between longfilter time constants for accurate estimation versus short filter timeconstants needed to track varying statistics due to fading.

In the Digital Audio Broadcasting (DAB) simulation, the OFDM symbol rateof 689.0625 Hz was chosen with a fading bandwidth of 13 Hz. Then thereciprocal of the fading bandwidth is about 53 symbols in this case. Afilter time constant of 16 symbols was chosen since this time constantmust be small compared to the fading time. Unfortunately, thestatistical estimation errors over this short filter time yielded poorperformance results for the adaptive weighting compared to what would bepossible with perfect statistical estimation. Even reducing the fadingbandwidth down to 3 Hz and increasing the filter time constant to 64samples left a significant loss.

Equations (16) and (17) reveal that, in effect, quantities raised to thefourth power are subtracted to yield smaller numbers. This situation ismost pronounced when the signal and noise powers are approximatelyequal, resulting in large estimation errors. Simulation results supportthis observation. Therefore another estimator is sought that does notrely upon subtraction fourth order statistics. The desired estimationtechnique should be designed to accommodate a fading bandwidth of up to13 Hz for maximum vehicle speeds in the FM band around 100 MHz.

The optimum soft-symbol weight to be applied before differentialdetection of QPSK can be described as a function of time (k index) andOFDM sub-carrier (n index). Similar to equation (14), this weight is:$\begin{matrix}{w_{k,n} = \frac{a_{k,n}}{\sqrt{{2a_{k,n}^{2}\sigma_{k,n}^{2}} + \sigma_{k,n}^{4}}}} & (18)\end{matrix}$

where a_(k,n) is the fading coefficient of the k^(th) symbol for then^(th) sub-carrier, and σ_(k,n) is the corresponding standard deviationof the noise or interference, both prior to differential detection.Notice that the weight of equation (18) is the square root of equation(14). This is a result of the reasonable assumption that the weightchanges slowly over the symbol-pair time used in the differentialdetection. In effect, the differential detection squares thepredetection weight of equation (18), which would result in equation(14). A method for improving the statistical estimates of equation (18)is sought.

Practical methods for estimating CSI and weights usingpre-differentially detected soft-symbols and weight also applied to thesoft decision symbol prior to differential detection will now bediscussed.

For moderate to high SNR, the weight of equation (18) can beconveniently approximated by: $\begin{matrix}{{{\lim\limits_{{SNR}\rightarrow\infty}w_{k}} = \frac{1}{\sqrt{2\sigma_{k}^{2}}}},} & (19)\end{matrix}$

where simple statistical measurements were used to estimate σ². However,simulation confirmed that this weight estimate performed poorly duringtimes when the SNR was very low due to fading interference. For example,the optimum weight would have suppressed the noisy samples more than thehigh SNR approximation to the weight. Therefore, another approximationwas sought which would estimate CSI statistics over a large SNR range.Furthermore the estimate should not be sensitive to a gaussian noise orinterference assumption, and should be estimated with sufficientaccuracy in a time (filter time constant) significantly less than thereciprocal of the fading bandwidth.

A simple and robust estimation technique evolved after simulation andsome experimentation. This estimation technique approximates thepreviously-defined weight expressions, but uses lower-order statisticalapproximations. This technique is described in the following 4 steps.

1. Create a sequence V_(k,n) for each QPSK sub-carrier consisting of themagnitudes of the complex soft decision outputs S_(k,n) from the matchedfilter for the n^(th) sub-carrier.

v _(k,n) =|s _(k,n)|  (20)

2. Create a sequence d_(k,n) consisting of the differences of successivetime samples of V_(k,n).

d _(k,n) =v _(k,n−v) _(k−1,n)  (21)

3. Filter the sequences V_(k,n) and d_(k,n) using second-order digitalIIR filters, then compensate for any differences in effective groupdelay to yield sequences filtv_(k,n) and filtd_(k,n). The time constantfor the filtv_(k,n) filter should be somewhat smaller than thereciprocal of the fading bandwidth, while the time constant for thefiltd_(k,n) filter can be somewhat larger. These sequences arerepresentative (approximately proportional) of the local mean andstandard deviation of the sequence V_(k,n).

4. The sequence of weights for the soft decisions for each sub-carrierto be applied prior to differential detection is defined as$\begin{matrix}{w_{k,n} = \frac{1}{{filtd}_{k,n} \cdot \left( {1 + \left( \frac{{filtd}_{k,n}}{{filtv}_{k,n} - {filtd}_{k,n}} \right)^{4}} \right)}} & (22)\end{matrix}$

To prevent numerical overflow, check to ensure that filtv_(k,n)>1.5·filtd_(k,n) in equation (22); otherwise, set the weight to zero.Simulation results verified that this weight yields good performanceunder a variety of channel impairments with fading and interference.

The values of filtd_(k,n) and filtv_(k,n) are estimated using filteringtechniques described next. Filtering is performed first for eachsub-carrier at the k^(th) symbol instant in time. Then the rows offiltd_(k,n) and filtv_(k,n) are simply updated across the Nsub-carriers. Equation (23) filters the sequences V_(k,n) with a timedelay of approximately 16 symbols, and equation (24) filters thesequences d_(k,n) with a time delay of approximately 64 symbols. Bothfilters have a zero frequency gain of nearly unity. $\begin{matrix}{{subv}_{k,n} = \frac{{960 \cdot {subv}_{{k - 1},n}} - {451 \cdot {subv}_{{k - 2},n}} + {3 \cdot v_{k,n}}}{512}} & (23) \\{{subd}_{k,n} = \frac{{16128 \cdot {subd}_{{k - 1},n}} - {7939 \cdot {subd}_{{k - 2},n}} + {3 \cdot d_{k,n}}}{8192}} & (24)\end{matrix}$

Additional filtering is performed across the N sub-carriers. Smoothingthe estimates across the N sub-carriers requires 3 passes of a simpleIIR filter. The first pass sets the appropriate initial condition of thefilter, but does not update the estimates. The direction of the secondpass is reversed from the first, while the third pass is reversed again.This results in an approximately symmetric (linear phase) filtercharacteristic which is desirable for providing the estimates on thecenter carrier. Although it is impossible to provide this symmetricfiltering for the sub-carriers at each end of the band, the impulseresponse “tails” are folded back into the active sub-carriers.

The first pass across the sub-carriers sets the initial values offiltv_(n−1) and filtd_(n−1) without replacing the time-filtered valuesfor each sub-carrier. The time index k is ignored here since it isunderstood that the filtering over the sub-carriers is performed overeach k^(th) OFDM symbol.

filtv _(n−1)<=(1−β)·filtv _(n−1) +β·subv _(n);

filtd _(n−1)<=(1−β)·filtd _(n−1) +β·subd _(n);

n=0,1, . . . N−1  (25)

The second pass smoothes the values across the filtered estimates foreach sub-carrier, subv and subd.

filtv _(n)<=(1−β)·filtv _(n=1) +β·subv _(n);

filtd _(n)<=(1−β)·filtd _(n=1) +β·subd _(n);

n=N−2, N−3, . . . 0  (26)

The third pass smoothes the frequency values again to achieve a nearlysymmetrical impulse response (except for the sub-carriers near theendpoints).

filtv _(n)<=(1−β)·filtv _(n−1) +β·fltv _(n);

filtd _(n)<=(1−β)·filtd _(n−1) +β·fltd _(n);

n=1,2, . . . N−1.  (27)

The resulting filtered values for filtv and filtd computed in equations(26) and (27) are used in equation (22) at each OFDM symbol time toyield the appropriate weight for each soft symbol prior to differentialdetection, but after matched filtering, in the receiver.

FIG. 1 is a diagram showing the steps of the method of this invention.Block 10 shows the step of receiving a plurality of sub-carriersmodulated by digital information. The sub-carriers are filtered as shownin block 12 to produce complex soft decision outputs. These outputs areused in block 14 to create a first sequence of the magnitudes of thecomplex soft decision outputs. Block 16 shows that the differencesbetween successive samples in the first sequence are determined. Asecond sequence of the differences between successive samples in thefirst sequence is created as shown in block 18. The first and secondsequences are filtered as in block 20 and compensated for differences ineffective group delay of the first and second sequences as in block 22to produce third and fourth sequences in block 24. The third and fourthsequences are used to determine a plurality of weights as shown in block26, and the plurality of weights are applied to the complex softdecision outputs as shown in block 28.

The above discussion relates to differentially detected QPSK. Thederivation for the weight using coherent detection of QPSK or (BPSK)would be similar to the technique discussed above for differentiallydetected QPSK. The only modification should be in the expressionpresented in equation (22). It can be predicted that the weight shouldbe of the form: $\begin{matrix}{w_{k,n} = \frac{{filtv}_{k,n} - {c \cdot {filtd}_{k,n}}}{{filtd}_{k,n}^{2}}} & (27)\end{matrix}$

where c is a constant to be defined by empirical methods.

Techniques for estimating the optimum soft-decision weight for QPSKsymbols prior to Viterbi decoding were described. These techniques applyto coherent and differential detection of single or multi-carrier (OFDM)QPSK, with and without multipath fading of the signal of interest or theinterferer. The fading cases can necessitate a compromise betweenaccurate CSI estimation and agility of the CSI to track the fadingsignal or noise components.

The application of soft-decision weighting for an OFDM system withindependently faded signal and noise (interference) can improve BERperformance. This weight is applied to the soft symbols prior todeinterleaving and Viterbi decoding. The optimal weight for each softsymbol over time and sub-carriers is estimated through an expressionusing filtered statistical estimates of channel state information (CSI)about the signal and noise components of the received symbols. The aboveCSI estimation and weighting techniques can apply to both coherent anddifferentially detected symbols, and to single and multi-carrier (OFDM)modulation in the presence of multipath fading and colored noisestatistics.

FIG. 2 is a functional block diagram showing the mapping and processingof bits through a portion of an FM receiver that operates in accordancewith the method of the invention. A plurality of OFDM carriers 30 arereceived and converted to bit streams on lines 32 by receiver circuit34. Circuit 34 includes a digitizer, carrier synchronization, symbolsynchronization, and matched filters all operating in accordance withwell known techniques to produce the bit streams on lines 36. Block 38represents the channel state estimates and weighting processes performedaccording to FIG. 1 to produce weighted bit streams on lines 40. Block42 shows that the bit streams are deallocated from the carriers anddelivered to a deinterleaver 44. The output of the deinterleaver ismultiplexed to a single bit stream and passed to a Viterbi decoder 46decodes the single bit stream. Soft-decision Viterbi decoding with(near) optimum soft-decision weighting for maximum ratio combining (MRC)for differentially detected QPSK sub-carrier symbols is employed tominimize losses over the channel. The output of the Viterbi decoder issubject to additional signal processing, which is not part of thepresent invention, and passed to output stages, as illustrated by block48, to produce the desired output from the receiver.

While the present invention has been described in terms of what are atpresent believed to be its preferred embodiments, it will be apparent tothose skilled in the art that various changes may be made to theembodiments described above without departing from the scope of theinvention as set forth in the following claims.

What is claimed is:
 1. A method for weighting orthogonal frequencydivision multiplexed soft symbols, said method comprising the steps of:receiving a plurality of sub-carriers modulated by digital information;filtering the sub-carriers to produce complex soft decision outputs;creating a first sequence of the magnitudes of said complex softdecision outputs; determining the differences between successive samplesin said first sequence; creating a second sequence of the differencesbetween successive samples in said first sequence; filtering said firstand second sequences to produce third and fourth sequences; using saidthird and fourth sequences to determine a plurality of weights; andapplying said plurality of weights to said complex soft decisionoutputs.
 2. The method of claim 1, wherein said sub-carriers aremodulated using quadrature phase shift keying.
 3. The method of claim 1,wherein said first and second sequences are filtered using a secondorder digital infinite impulse response filter.
 4. The method of claim1, wherein: said third sequence has a time constant smaller than thereciprocal of the fading bandwidth of plurality of sub-carriers; andsaid fourth sequence has a time constant larger than the reciprocal ofthe fading bandwidth of plurality of sub-carriers.
 5. The method ofclaim 1, wherein the step of filtering said first and second sequencesfurther comprises the step of compensating for differences in effectivegroup delay of said first and second sequences to produce third andfourth sequences.
 6. The method of claim 1, wherein said plurality ofweights are determined using the formula:$w_{k,n} = \frac{1}{{filtd}_{k,n} \cdot \left( {1 + \left( \frac{{filtd}_{k,n}}{{filtv}_{k,n} - {filtd}_{k,n}} \right)^{4}} \right)}$

wherein w_(k,n) represents said plurality of weights, filtv_(k,n)represents said third sequence, filtd_(k,n) represents said fourthsequence, k identifies one of said symbols, and n identifies one of saidsub-carriers.
 7. The method of claim 6, whereinfiltv_(k,n)>1.5·filtd_(k,n), then w_(k,n) is set to zero.
 8. A radioreceiver comprising: means for receiving a plurality of sub-carriersmodulated by digital information; means for filtering the sub-carriersto produce complex soft decision outputs; means for creating a firstsequence of the magnitudes of said complex soft decision outputs; meansfor determining the differences between successive samples in said firstsequence; means for creating a second sequence of the differencesbetween successive samples in said first sequence; means for filteringsaid first and second sequences to produce third and fourth sequences;means for using said third and fourth sequences to determine a pluralityof weights; and means for applying said plurality of weights to saidcomplex soft decision outputs.
 9. The receiver of claim 8, wherein saidsub-carriers are modulated using quadrature phase shift keying.
 10. Thereceiver of claim 8, wherein said first and second sequences arefiltered using a second order digital infinite impulse response filter.11. The receiver of claim 8, wherein: said third sequence has a timeconstant smaller than the reciprocal of the fading bandwidth ofplurality of sub-carriers; and said fourth sequence has a time constantlarger than the reciprocal of the fading bandwidth of plurality ofsub-carriers.
 12. The receiver of claim 8, wherein the means forfiltering said first and second sequences further comprises means forcompensating for differences in effective group delay of said first andsecond sequences to produce third and fourth sequences.
 13. The receiverof claim 8, wherein said plurality of weights are determined using theformula:$w_{k,n} = \frac{1}{{filtd}_{k,n} \cdot \left( {1 + \left( \frac{{filtd}_{k,n}}{{filtv}_{k,n} - {filtd}_{k,n}} \right)^{4}} \right)}$

where w_(k,n) represents said plurality of weights, filtv_(k,n)represents said third sequence, filtd_(k,n) represents said fourthsequence, k identifies a symbol in said digital information, and nidentifies one of said sub-carriers.
 14. The receiver of claim 13,wherein filtv_(k,n>)1.5·filtv_(k,n), then W_(k,n) is set to zero.